An Anderson Acceleration Inspired VBIM for Solving the Electromagnetic Inverse Scattering Problems

This article proposes an adaptive damping Anderson acceleration (ADAA) method that augments the variational Born iterative method (VBIM) for solving the electromagnetic inverse scattering problems (ISPs). Traditionally, the Anderson acceleration (AA) method accelerates convergence in fixed-point iterations by extrapolating solutions from a linear combination of previous iterations. However, different from the fixed-point iteration, whose operator is definite, the mapping operator in the VBIM is approximate and noncontractive. A necessary modification is made by substituting the gradient-acceptance-based strategy in standard AA to the total-quantity-acceptance-based strategy. Additionally, considering the later work in AA demonstrates a damping factor boosts the convergence speed of AA, we present an adaptive damping strategy to further augment the inversion’s convergence rate. The dual-enhancements significantly improve both the speed and robustness of convergence. From a mathematical perspective, the VBIM-ADAA method seeks an exact data equation solution in a subspace spanned by previous regularization solutions during each iteration. Furthermore, the robustness facilitated by VBIM-ADAA permits a broader range of choices for the regularization parameter. By leveraging QR factorization (via the Gram-Schmidt process), we analyze the VBIM-ADAA’s characteristics under different mapping operators. Extensive numerical experiments, involving both synthetic and real-world data, verify the superior convergence, robustness, and better accuracy of the VBIM-ADAA compared to the conventional VBIM. Moreover, numerical experiments demonstrate that the computational time consumed by the ADAA is negligible, which makes it a practical and efficient method for solving ISPs.